Monday, August 3, 2015

Wave function can be just our knowledge

Interpretations of quantum mechanics can disagree about whether the wave function Psi is a direct reflection of reality (ontology, ontic) or just a representation of our knowledge (epistemology, epistemic).

Some would also say to "shut up and calculate", and would be dismissive of such philosophical distinctions. Bohr would say that anytime you write formulas on paper, you are just trying to express our knowledge about a system.

Building upon the Harrigan‐Spekkens analysis, the PBR paper (Pusey, Barrett and Rudolph 2012) raises the question of whether a Ψ‐epistemic interpretation of the Ψ‐function is consistent with QM. According to the theorem proved in the paper, it is not, namely, if the epistemic interpretation is accepted and an overlap of the supports of two distinct probability distributions (corresponding to two distinct quantum states) is allowed, a violation of the predictions QM follows. PBR conclude that QM is not amenable to the epistemic interpretation. This surprising result has immediately attracted a great deal of attention. Most readers have taken the theorem at face value: The Ψ‐epistemic interpretation is indeed ruled out by the theorem and consequently, the remaining option is the Ψ‐ontic interpretations. In other words, the PBR theorem has been advertised as supporting a realist interpretation rather than an epistemic interpretation of Ψ. ...

What if we go radically epistemic and deny the assumption of definite physical states? In that case we take QM to be mute about the physical state of the system, interpreting it instead along the lines of Schrodinger, Pitowsky, Bub, Fuchs and others have suggested, as a maximal catalog of possible measurement results, a betting algorithm, a book‐keeping device. This option is left untouched by the PBR theorem. Not only is it not undermined by it, to the contrary, in ruling out a more classical probabilistic interpretation, which presupposes the existence of the ‘real’ state of the system, the PBR theorem in fact strengthens the radical epistemic interpretation.

So this paper made a big splash because the authors claimed to be disproving an epistemic interpretation, but it does nothing of the kind. It only gives an argument against a hidden variable theory that no one believed in anyway.

The original title to the PBR paper was The quantum state cannot be interpreted statistically, and was accepted for publication in Nature, a very high status journal. This raised eyebrows as the quantum state wave function has been interpreted statistically for 80+ years, and nothing short of a startling Nobel-Prize-winning discovery can change that.

But the title was incorrect use of terminology, and all they had was an argument against replacing quantum mechanics with a hidden variable theory of the type that had been considered and rejected 80 years ago. The argument had nothing to do with statistical interpretations. The title had to be changed, and the paper was published in a lesser journal.